Tracking of sinusoidal commands and/or rejection of sinusoidal disturbances are desirable control objectives in many applications. Use of a proportional-integral-derivative (PID) controller does not ensure zero steady-state error in such cases. By introducing an infinite gain to the loop at its center frequency, a resonant (R) controller ensures that such an objective is achieved.
For digital controllers, field programmable gate arrays (FPGAs) are desirable for applications that demand high volume of calculations with time constraints, such as in power electronics. Such applications are becoming more important as the size and complexity of power electronic designs become critical. An example is a microinverter, which requires compact, reliable, and robust design. FPGA implementations need fixed-point calculations which require more attention in the design.
A digital resonant controller suffers from difficulties at high sampling frequencies with limited number of bits (NB) (i.e., fixed-point implementation). In such cases, an accurate realization of the controller may demand extremely high NB. Those requirements are particularly desirable in power electronic circuits with compact size. The δ operator concept is able to overcome this issue and provide an alternative representation for the controller that is implementable using lower word length. This method has a parameter Δ which must be properly designed to establish the desired tradeoff between truncation errors and word length. Another challenge with the δ operator method concerns applications where frequency fluctuations can be relatively high. The various existing methods for frequency-adaptive R controller such as in [1] and [2] cannot be applied without serious challenges. For example, the frequency appears in all the controller's parameters and, to make the controller frequency-adaptive, all parameters must be made adaptive. This is particularly demanding when a fixed-point implementation is desired.